Search: id:A086246
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%I A086246
%S A086246 0,1,1,1,2,4,9,21,51,127,323,835,2188,5798,15511,41835,113634,310572,
%T A086246 853467,2356779,6536382,18199284,50852019,142547559,400763223,
%U A086246 1129760415,3192727797,9043402501,25669818476,73007772802,208023278209
%N A086246 Expansion of (1+x-sqrt(1-2x-3x^2))/2 in powers of x.
%C A086246 A variant of the Motzkin numbers: see A001006 for the main entry.
%C A086246 Equals row sums of triangle A144218 starting with "1". [From Gary W. 
               Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008]
%C A086246 Starting (1, 1, 1,...) = inverse binomial transform of A014137: (1, 2, 
               4, 9, 23, 65,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Apr 02 2009]
%F A086246 Series reversion of g.f. A(x) is -A(-x).
%F A086246 a(n)+a(n-1)=a(0)*a(n)+a(1)*a(n-1)+...+a(n)*a(0), n>2.
%F A086246 G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=x-y-x*y+x^2+y^2.
%F A086246 G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=(y^2-y^3)-(x^2+x^3).
%F A086246 G.f.: (1+x-sqrt(1-2x-3x^2))/2.
%F A086246 G.f. A(x) satisfies A(x) = x+C(xA(x)) where C(x) is g.f. for Catalan 
               numbers A000108 (offset 1).
%o A086246 (PARI) a(n)=polcoeff((1+x-sqrt(1-2*x-3*x^2+x*O(x^n)))/2,n)
%Y A086246 a(n+2)=A001006(n).
%Y A086246 Cf. A144218 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 14 2008]
%Y A086246 A014137 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2009]
%Y A086246 Sequence in context: A094288 A168051 A166587 this_sequence A168049 A001006 
               A027057
%Y A086246 Adjacent sequences: A086243 A086244 A086245 this_sequence A086247 A086248 
               A086249
%K A086246 nonn
%O A086246 0,5
%A A086246 Michael Somos, Jul 13 2003

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